Secretary of State Hillary Rodham Clinton arrives in the Mideast for talks. A cease-fire agreement appears close but elusive. The toll climbs on both sides.

GAZA CITY — Secretary of State Hillary Rodham Clinton pressed for an end to rocket attacks on Israel and a durable regional peace as she arrived in the Middle East to join efforts to end a week of fighting between Israel and the Islamist militant group Hamas.

An agreement appeared close late Tuesday but proved elusive, and in the meantime violence continued. Hamas fired two more rockets toward Jerusalem but caused no damage or injuries. But rocket and mortar fire from the Gaza Strip killed an Israeli soldier and a Bedouin resident in southern Israel, increasing the Israeli death toll to five.

Israel responded with airstrikes on what it said were rocket-launching squads, underground weapons caches, a Hamas-owned bank, smuggling tunnels and other targets. By late Tuesday, Hamas' Health Ministry said, the Palestinian death toll in the conflict had increased to 133, including many militants but also 33 children. It said more than 1,000 people had been wounded.

Clinton, who was visiting Asia with President Obama, traveled to Jerusalem and met late Tuesday with Israeli Prime Minister Benjamin Netanyahu. Obama and Clinton had been making frequent calls to Middle East leaders to press for an end to the fighting, but aides said the calls left Obama convinced that the U.S. needed to be more deeply involved.

"The rocket attacks from terrorist organizations inside Gaza on Israeli cities and towns must end and a broader calm restored," Clinton said. "The goal must be a durable outcome that promotes regional stability and advances the security and legitimate aspirations of Israelis and Palestinians alike."

Netanyahu said he preferred a "long-term solution" through diplomacy, but that Israel "will have to take whatever actions necessary to defend its people."

Neither side appears to want to see an Israeli ground incursion. After seven days of fighting, many Gaza residents said they were ready for life to return to normal.

But in addition to its airstrikes, Israel sent hundreds of panicked residents in northern and eastern Gaza City fleeing their homes over fears of an impending ground assault. Israeli aircraft dropped leaflets warning residents to evacuate immediately and specifying which streets to use to avoid harm, a move that led many to fear an assault was imminent. Previously Israel's leaflets had included only general warnings for residents to stay away from Hamas buildings or officials.

Hamas officials had been hoping to finalize an agreement by Tuesday night, predicting a cease-fire would take effect by midnight. But as the evening wore on, Israeli and Egyptian officials began downplaying expectations, warning that no deal had been signed. All sides hinted that a deal might be reached Wednesday.

According to one senior Hamas official, the parties reached a "major breakthrough" Tuesday when Israel agreed to halt attacks against Gaza, stop targeted killings of Hamas leaders and ease border restrictions.

Israel has not commented on details of any possible agreement. It is seeking an end to the rocket fire by Gaza militants and assurances — backed up by Egypt and the international community — that Hamas won't be allowed to rebuild the weapons caches that Israel has destroyed.

The talks are being conducted through Turkish and Egyptian intermediaries in Cairo because Israel and Hamas don't formally recognize each other.

Ben Rhodes, the deputy national security advisor, told reporters traveling with the president that Obama had not asked Netanyahu to hold off on sending ground troops into Gaza. State Department and White House officials carefully avoided using the term "cease-fire," suggesting that they may be satisfied with something less than a formal halt to hostilities, at least for now.

If a cease-fire, or something close to it, is announced, analysts in Washington said, Clinton could use American influence to pressure the parties to adhere to it.

"She's there as a guarantor," said Robert Danin, a former senior State Department official in the Middle East who is now an analyst with the nonpartisan Council on Foreign Relations. After Jerusalem, Clinton was scheduled to visit Palestinian officials in Ramallah and then travel to Cairo.

For Israel, a deal may be its best bet at ending the barrage of rockets from Gaza militants. One million Israelis spent much of the last week scrambling for the safety of bomb shelters under a shower of more than 1,000 rockets.

Leaders of key regional powers such as Egypt and Turkey have sharply criticized Israel, and that appears to have emboldened Hamas.

Depending on the details of an agreement, Hamas, which Washington and many Western countries regard as a terrorist organization, might emerge with more international credibility and might be able to claim the truce as a victory for its pursuit of Palestinian independence through armed struggle rather than diplomacy. But that would also obligate Hamas to act as a serious negotiating partner.